1. BINARY SEARCH ALGORITHM
This only applies to a list of names in alphabetical order or a list of
numbers in increasing order.
Unordered lists would have a sorting algorithm applied first.
This algorithm concentrates on the midpoint of an ever reducing list.
We define the midpoint of a list of N names, numbered
N1, N1+1,...,N2 as [(N1+N2)/2]
where [x] = the smallest integer greater than or equal to x
We wish to search the list for a name, Fred, say.

2. Step 1
The algorithm compares Fred with the middle name in the list.
Either a) the name Fred is found to be at this position,
or b) the name Fred occurs before the middle of the list
or c) the name Fred occurs after the middle of the list
Step 2
If a) occurs, the search is over.
If b) occurs, the search continues with Step 1 on a reduced list
consisting of those names before the middle name.
If c) occurs, the search continues with Step 1 on a reduced list
consisting of those names after the middle name.
Stop when Fred has been found or when it has been shown that Fred
does not appear on the list.
At each stage half of the remaining list is discarded (hence the name
of the algorithm).

3. 1 Bennett 6 Laing 2 Blackstock 3 Brown 4 Ebenezer 5 Fowler 9 Saludo
Find the name Robinson in the list below:
Middle name:
1 Bennett
6 Laing
2 Blackstock
Robinson is after Laing
So delete names 1-6
3 Brown
This leaves names 7 to 10
4 Ebenezer
Middle name:
5 Fowler
9 Saludo
6 Laing
Robinson is before Saludo
So delete names 9-10
7 Leung
This leaves names 7 to 8
Middle name:
8 Robinson
8 Robinson
9 Saludo
has been found!
10 Scadding

4. 1 Bennett 6 Laing 2 Blackstock 3 Brown 4 Ebenezer 3 Brown 5 Fowler
Find the name Davis in the list below:
Middle name:
1 Bennett
6 Laing
2 Blackstock
Davis is before Laing
So delete names 6-10
3 Brown
This leaves names 1 to 5
Middle name:
4 Ebenezer
3 Brown
5 Fowler
Davis is after Brown
So delete names 1-3
6 Laing
This leaves names 4 and 5
Middle name:
7 Leung
5 Fowler
8 Robinson
9 Saludo
Davis is before Fowler
So delete name 5
Only one name left (Ebenezer) and it is not Davis
10 Scadding
Hence we conclude that Davis is not on the list